Theory of Computing Systems最新文献_第5页

Quantum Algorithm for Lexicographically Minimal String Rotation 字典最小字符串旋转的量子算法

4区计算机科学

Theory of Computing Systems Pub Date : 2023-10-24 DOI: 10.1007/s00224-023-10146-8

Qisheng Wang, Mingsheng Ying

{"title":"Quantum Algorithm for Lexicographically Minimal String Rotation","authors":"Qisheng Wang, Mingsheng Ying","doi":"10.1007/s00224-023-10146-8","DOIUrl":"https://doi.org/10.1007/s00224-023-10146-8","url":null,"abstract":"Abstract Lexicographically minimal string rotation (LMSR) is a problem to find the minimal one among all rotations of a string in the lexicographical order, which is widely used in equality checking of graphs, polygons, automata and chemical structures. In this paper, we propose an $$O(n^{3/4})$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:msup> <mml:mi>n</mml:mi> <mml:mrow> <mml:mn>3</mml:mn> <mml:mo>/</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> quantum query algorithm for LMSR. In particular, the algorithm has average-case query complexity $$O(sqrt{n} log n)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:msqrt> <mml:mi>n</mml:mi> </mml:msqrt> <mml:mo>log</mml:mo> <mml:mi>n</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , which is shown to be asymptotically optimal up to a polylogarithmic factor, compared to its $$Omega left( sqrt{n/log n}right) $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>Ω</mml:mi> <mml:mfenced> <mml:msqrt> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>/</mml:mo> <mml:mo>log</mml:mo> <mml:mi>n</mml:mi> </mml:mrow> </mml:msqrt> </mml:mfenced> </mml:mrow> </mml:math> lower bound. Furthermore, we show that our quantum algorithm outperforms any (classical) randomized algorithms in both worst and average cases. As an application, it is used in benzenoid identification and disjoint-cycle automata minimization.","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":"144 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135273543","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 5

Representing the Integer Factorization Problem Using Ordered Binary Decision Diagrams 用有序二元决策图表示整数分解问题

4区计算机科学

Theory of Computing Systems Pub Date : 2023-10-19 DOI: 10.1007/s00224-023-10147-7

David E. Brown, David Skidmore

引用次数: 0

Toward Online Mobile Facility Location on General Metrics 基于一般指标的在线移动设施定位

4区计算机科学

Theory of Computing Systems Pub Date : 2023-10-06 DOI: 10.1007/s00224-023-10145-9

Abdolhamid Ghodselahi, Fabian Kuhn

{"title":"Toward Online Mobile Facility Location on General Metrics","authors":"Abdolhamid Ghodselahi, Fabian Kuhn","doi":"10.1007/s00224-023-10145-9","DOIUrl":"https://doi.org/10.1007/s00224-023-10145-9","url":null,"abstract":"Abstract We introduce an online variant of mobile facility location (MFL) (introduced by Demaine et al. (SODA 258–267 2007)). We call this new problem online mobile facility location (OMFL). In the OMFL problem, initially, we are given a set of k mobile facilities with their starting locations. One by one, requests are added. After each request arrives, one can make some changes to the facility locations before the subsequent request arrives. Each request is always assigned to the nearest facility. The cost of this assignment is the distance from the request to the facility. The objective is to minimize the total cost, which consists of the relocation cost of facilities and the distance cost of requests to their nearest facilities. We provide a lower bound for the OMFL problem that even holds on uniform metrics . A natural approach to solve the OMFL problem for general metric spaces is to utilize hierarchically well-separated trees (HSTs) and directly solve the OMFL problem on HSTs. In this paper, we provide the first step in this direction by solving a generalized variant of the OMFL problem on uniform metrics that we call G-OMFL. We devise a simple deterministic online algorithm and provide a tight analysis for the algorithm. The second step remains an open question. Inspired by the k -server problem, we introduce a new variant of the OMFL problem that focuses solely on minimizing movement cost. We refer to this variant as M-OMFL. Additionally, we provide a lower bound for M-OMFL that is applicable even on uniform metrics.","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135350992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Weighted Tree Automata with Constraints 带约束的加权树自动机

4区计算机科学

Theory of Computing Systems Pub Date : 2023-10-03 DOI: 10.1007/s00224-023-10144-w

Andreas Maletti, Andreea-Teodora Nász

引用次数: 0

b-Coloring Parameterized by Clique-Width 由团宽度参数化的b-着色

4区计算机科学

Theory of Computing Systems Pub Date : 2023-09-23 DOI: 10.1007/s00224-023-10132-0

Lars Jaffke, Paloma T. Lima, Daniel Lokshtanov

引用次数: 0

Small Vertex Cover Helps in Fixed-Parameter Tractability of Graph Deletion Problems over Data Streams 小顶点覆盖有助于数据流上图删除问题的固定参数可跟踪性

4区计算机科学

Theory of Computing Systems Pub Date : 2023-09-20 DOI: 10.1007/s00224-023-10136-w

Arijit Bishnu, Arijit Ghosh, Sudeshna Kolay, Gopinath Mishra, Saket Saurabh

{"title":"Small Vertex Cover Helps in Fixed-Parameter Tractability of Graph Deletion Problems over Data Streams","authors":"Arijit Bishnu, Arijit Ghosh, Sudeshna Kolay, Gopinath Mishra, Saket Saurabh","doi":"10.1007/s00224-023-10136-w","DOIUrl":"https://doi.org/10.1007/s00224-023-10136-w","url":null,"abstract":"Abstract In the study of parameterized streaming complexity on graph problems, the main goal is to design streaming algorithms for parameterized problems such that $$mathcal {O}(f(k) log ^{mathcal {O}(1)} n)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:mi>f</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>k</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:msup> <mml:mo>log</mml:mo> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:msup> <mml:mi>n</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> space is enough, where f is an arbitrary computable function depending only on the parameter k . However, in the past few years very few positive results have been established. Most of the graph problems that do have streaming algorithms of the above nature are ones where localized checking is required, like Vertex Cover or Maximum Matching parameterized by the size k of the solution we are seeking. Chitnis et al. (SODA’16) have shown that many important parameterized problems that form the backbone of traditional parameterized complexity are known to require $$Omega (n)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>Ω</mml:mi> <mml:mo>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> bits of storage for any streaming algorithm; e.g. Feedback Vertex Set , Even Cycle Transversal , Odd Cycle Transversal , Triangle Deletion or the more general $$mathcal{F}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>F</mml:mi> </mml:math> - Subgraph Deletion when parameterized by solution size k . Our contribution lies in overcoming the obstacles to efficient parameterized streaming algorithms in graph deletion problems by utilizing the power of parameterization. We focus on the vertex cover size K as the parameter for the parameterized graph deletion problems we consider. In this work, we consider the four most well-studied streaming models: the Ea , Dea , Va (vertex arrival) and Al (adjacency list) models. Surprisingly, the consideration of vertex cover size K in the different models leads to a classification of positive and negative results for problems like $$mathcal{F}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>F</mml:mi> </mml:math> - Subgraph Deletion and $$mathcal{F}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>F</mml:mi> </mml:math> - Minor Deletion .","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136308259","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Well-Covered Graphs With Constraints On $$Delta $$ And $$delta $$ 在$$Delta $$和上有约束的完备图 $$delta $$

IF 0.5 4区计算机科学

Theory of Computing Systems Pub Date : 2023-08-28 DOI: 10.1007/s00224-023-10140-0

Vadim E. Levit, David Tankus

引用次数: 0

Correction to: Dynamic Multiple-Message Broadcast: Bounding Throughput in the Affectance Model 修正:动态多消息广播:影响模型中的边界吞吐量

IF 0.5 4区计算机科学

Theory of Computing Systems Pub Date : 2023-08-28 DOI: 10.1007/s00224-023-10143-x

Dariusz R. Kowalski, Miguel A. Mosteiro, Kevin Zaki

引用次数: 0

The Space Complexity of Sum Labelling 和标记的空间复杂度

4区计算机科学

Theory of Computing Systems Pub Date : 2023-08-25 DOI: 10.1007/s00224-023-10130-2

Henning Fernau, Kshitij Gajjar

{"title":"The Space Complexity of Sum Labelling","authors":"Henning Fernau, Kshitij Gajjar","doi":"10.1007/s00224-023-10130-2","DOIUrl":"https://doi.org/10.1007/s00224-023-10130-2","url":null,"abstract":"Abstract A graph is called a sum graph if its vertices can be labelled by distinct positive integers such that there is an edge between two vertices if and only if the sum of their labels is the label of another vertex of the graph. Most papers on sum graphs consider combinatorial questions like the minimum number of isolated vertices that need to be added to a given graph to make it a sum graph. In this paper, we initiate the study of sum graphs from the viewpoint of computational complexity. Notice that every n -vertex sum graph can be represented by a sorted list of n positive integers where edge queries can be answered in $$mathscr {O}(log n)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:mo>log</mml:mo> <mml:mi>n</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> time. Therefore, upper-bounding the numbers used as vertex labels also upper-bounds the space complexity of storing the graph in the database. We show that every n -vertex, m -edge, d -degenerate graph can be made a sum graph by adding at most m isolated vertices to it, such that the largest numbers used as vertex labels grows as $$mathscr {O}(n^2d)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:msup> <mml:mi>n</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mi>d</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> . This enables us to store the graph using $$mathscr {O}(mlog n)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:mi>m</mml:mi> <mml:mo>log</mml:mo> <mml:mi>n</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> bits of memory. For sparse graphs (graphs with $$mathscr {O}(n)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> edges), this matches the trivial lower bound of $$Omega (nlog n)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>Ω</mml:mi> <mml:mo>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>log</mml:mo> <mml:mi>n</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> . As planar graphs and forests have constant degeneracy, our result implies an upper bound of $$mathscr {O}(n^2)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:msup> <mml:mi>n</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> on their label numbers. The previously best known upper bound on the numbers needed for labelling general graphs with the minimum number of isolated vertices was $$mathscr {O}(4^n)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:msup> <mml:mn>4</mml:mn> <mml:mi>n</mml:mi> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , due to Kratochvíl, Miller & Nguyen (2001). Furthermore, ","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135236029","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Improved Lower and Upper Bounds on the Tile Complexity of Uniquely Self-Assembling a Thin Rectangle Non-Cooperatively in 3D 改进的三维非合作薄型矩形唯一自组装贴图复杂度下界和上界

4区计算机科学

Theory of Computing Systems Pub Date : 2023-08-23 DOI: 10.1007/s00224-023-10137-9

David Furcy, Scott M. Summers, Logan Withers

引用次数: 2